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The feedback heating from active galactic nuclei (AGNs) in massive galaxies and galaxy clusters can be thought of as a naturally occurring control system which plays a significant role in regulating both star formation rates and the X-ray luminosity of the surrounding hot gas. In the simplest case, negative feedback can be viewed as a system response that is ‘optimized’ to minimize deviations from equilibrium, such that the system rapidly evolves towards a steady state. However, a general solution of this form appears to be incompatible with radio observations which indicate intermittent AGN...

The feedback heating from active galactic nuclei (AGNs) in massive galaxies and galaxy clusters can be thought of as a naturally occurring control system which plays a significant role in regulating both star formation rates and the X-ray luminosity of the surrounding hot gas. In the simplest case, negative feedback can be viewed as a system response that is ‘optimized’ to minimize deviations from equilibrium, such that the system rapidly evolves towards a steady state. However, a general solution of this form appears to be incompatible with radio observations which indicate intermittent AGN outbursts. Here, we explore an energetically favourable scenario in which feedback is required to both balance X-ray gas cooling and minimize the sum of the energy radiated by the gas and the energy injected by the AGN. This specification is equivalent to ensuring that AGN heating balances the X-ray gas cooling with the minimum black hole growth. It is shown that minimum energy heating occurs in discrete events and not at a continuous, constant level. Furthermore, systems with stronger feedback experience proportionally more powerful heating events, but correspondingly smaller duty cycles. Interpreting observations from this perspective would imply that stronger feedback occurs in less-massive objects – elliptical galaxies rather than galaxy clusters. One direct consequence of this effect would be that AGN heating events are sufficiently powerful to expel hot gas from the gravitational potential of a galaxy, but not a galaxy cluster, which is consistent with theoretical explanations for the steepening of the LX–T relation at temperatures below 1–2 keV.